[gmx-users] how to calculate kinetic constant?

rajat desikan rajatdesikan at gmail.com
Sun Oct 6 09:14:56 CEST 2013

```Hi Chris,
The activation energy is obtained from the PMF well depth. So that leaves
two variables k and A. If we get K at say 5 temepratures, and plot ln(k)
vs. 1/T, the intercept will give us A. From that, at the temperature of
interest, we can back out k.

I will dig up the paper I saw this in. It was a really long time ago though.

On Sun, Oct 6, 2013 at 2:33 AM, Christopher Neale <
chris.neale at mail.utoronto.ca> wrote:

> Dear Rajat:
>
> I just checked the first two papers that you mentioned and they both get
> kinetics from standard equilibrium simulations. As for the Arrhenius law,
> with k, A, and the energy of activation (Ea) all unknown for each T, how do
> you obtain a unique solution for k given T ? Even if you assume that Ea is
> some function of the maximum of your PMF (which is not always true), I
> presume that you can only then get the relationship between k and A, not
> the absolute value of k, even with information from many temperatures.
> However, I've never worked on this directly. Can you provide a reference so
> that I can take a look?
>
> Thank you,
> Chris.
>
> -- original message --
>
> Hi Chris,
> I have never done this and I may be missing something. But here is what I
> think.
> I have seen a few papers use the Arrhenius law, k=A*exp
> (-deltaG/kB*T)...-deltaG/kB*T can be obtained from the PMF...Now, if you do
> this for different temperatures, you can back out the activation energy and
> hence the rate constant.
>
> Regards,
>
>
> On Sat, Oct 5, 2013 at 11:44 PM, Christopher Neale <
> chris.neale at mail.utoronto.ca> wrote:
>
> > If you want K_on and K_off, then I think you need to look at long-time
> > equilibrium simulations or massively repeated simulations connected with
> a
> > MSM. Beyond that, I believe that you will need to understand all of the
> > important free energy barriers in all degrees of freedom (hard, to say
> the
> > least).
> >
> > Rajat: how are you going to compute kinetics from a PMF? Barriers in
> > orthogonal degrees of freedom don't show up on your PMF but can greatly
> > affect the kinetics. Even relatively minor roughness of the
> > multidimensional free energy surface and off-pathway kinetic traps are
> > going to affect the kinetics but not the PMF. Some people have tried to
> > circumvent this limitation by using the PMF in addition to computing the
> > local diffusion at each small section of the order parameter (e.g.,
> > http://www.nature.com/nnano/journal/v3/n6/full/nnano.2008.130.html ) but
> > unless there is excellent sampling overlap and lots of transitions
> between
> > all relevant states, I see this as a way to calculate an upper bound of
> > rates that I think could easily be much slower. See, for example,
> > http://pubs.acs.org/doi/abs/10.1021/jp045544s . Finally, I am not sure
> > how rates can be usefully extracted from a non-equilibrium method like
> REMD.
> >
> > Unless I missed it, the paper that David cites:
> > http://pubs.acs.org/doi/abs/10.1021/ct400404q doesn't compute kinetics.
> >
> > Perhaps the OP can provide more information on what they are trying to
> > obtain, exactly.
> >
> > Chris.
> >
> > -- original message --
> >
> > If you are looking at binding/unbinding as a function of temperature
> > (hopefully with REMD), you can use g_kinetics. If you are looking at
> > unbinding/binding events in a single simulation with temperature, etc
> > constant (no annealing), you will need to calculate binding
> probabilities,
> > from which you can back out a rate constant. A simple google search gave
> me
> > these papers (http://www.pnas.org/content/90/20/9547.full.pdf,
> > http://pubs.acs.org/doi/abs/10.1021/jp037422q)
> >
> > Of course, the best approach is to calculate the PMF and back out the
> rate
> > constant from the free energy. Hope that helps.
> >
> --
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--
Rajat Desikan (Ph.D Scholar)
Prof. K. Ganapathy Ayappa's Lab (no 13),
Dept. of Chemical Engineering,
Indian Institute of Science, Bangalore

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